Two adjacent sides of parallelogram are 24 cm and 18 cm. If the distance between the longer sides is 12 cm, find the distance between shorter sides.

Answer

To solve the problem step by step, we will find the distance between the shorter sides of the parallelogram using the given dimensions.

### Step 1: Identify the given values
We have a parallelogram with:
- Length of one side (base) = 24 cm (longer side)
- Length of the adjacent side = 18 cm (shorter side)
- Distance (height) between the longer sides = 12 cm

### Step 2: Calculate the area of the parallelogram using the longer side
The area \( A \) of a parallelogram can be calculated using the formula:
\[ A = \text{base} \times \text{height} \]
Using the longer side as the base:
\[ A = 24 \, \text{cm} \times 12 \, \text{cm} = 288 \, \text{cm}^2 \]

### Step 3: Set up the equation for the area using the shorter side
Now, we will calculate the area using the shorter side (18 cm) as the base. Let \( h \) be the distance between the shorter sides (the height corresponding to the base of 18 cm).
\[ A = \text{base} \times \text{height} = 18 \, \text{cm} \times h \]
Since we already calculated the area to be 288 cm², we can set up the equation:
\[ 288 = 18 \times h \]

### Step 4: Solve for \( h \)
To find \( h \), we rearrange the equation:
\[ h = \frac{288}{18} \]
Calculating this gives:
\[ h = 16 \, \text{cm} \]

### Step 5: Conclusion
The distance between the shorter sides of the parallelogram is 16 cm.